Question

For what value of x is the mode of the data 24, 15, 90, 23, 27, 26, 22, 25, 20, x + 3 found 25? Using this value of x, find the median.

Answer 1

ANSWER:
Given: Mode = 25
∴ 25 occurs maximum number of times.
Arranging the given data in ascending order:
15, 20, 22, 23, 24, x + 3, 25, 26, 27, 40
∴ x + 3 = 25
⇒ x = 25 − 3
⇒ x = 22
Hence, the value of x is 22.
Arranging the given data in ascending order:
15, 20, 22, 23, 24, 25, 25, 26, 27, 40
Number of terms = 10 (even)
∴ Median=mean of n/2th term and n/2+1th term
=mean of 24 and 25
=$\frac{(24+25)}{2}$
=mean of $\frac{14}{40}$th term and $\frac{10}{2}$+1th term

=24.5

Hence, the median is 24.5 .